Vladimir I. Arnold, Ilia Itenberg, Viatcheslav Kharlamov, Eugenii I. Shustin, Gerald G. Gould
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images.
At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century).
In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you...
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images....
The first two chapters of this book have been thoroughly revised and sig- nificantly expanded. Sections have been added on elementary methods of in- tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quasi-homogeneous equations), on first-order linear and quasi-linear partial differential equations, on equations not solved for the derivative, and on Sturm's theorems on the zeros of second-order linear equa- tions. Thus the new edition contains all the questions of the current syllabus in the theory of ordinary differential equations. In discussing...
The first two chapters of this book have been thoroughly revised and sig- nificantly expanded. Sections have been added on elementary methods of in- t...
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point...
